A geometric characterization of the upper bound for the span of the jones polynomial

Gonzalez Meneses, Juan y Gonzalez Manchon, Pedro Maria (2011). A geometric characterization of the upper bound for the span of the jones polynomial. "Journal of Knot Theory and Its Ramifications", v. 20 (n. 7); pp. 1059-1071. ISSN 0218-2165. https://doi.org/10.1142/S0218216511009005.

Descripción

Título: A geometric characterization of the upper bound for the span of the jones polynomial
Autor/es:
  • Gonzalez Meneses, Juan
  • Gonzalez Manchon, Pedro Maria
Tipo de Documento: Artículo
Título de Revista/Publicación: Journal of Knot Theory and Its Ramifications
Fecha: Julio 2011
Volumen: 20
Materias:
Escuela: E.U.I.T. Industrial (UPM) [antigua denominación]
Departamento: Matemática Aplicada
Licencias Creative Commons: Reconocimiento - Sin obra derivada - No comercial

Texto completo

[img]
Vista Previa
PDF (Document Portable Format) - Se necesita un visor de ficheros PDF, como GSview, Xpdf o Adobe Acrobat Reader
Descargar (175kB) | Vista Previa

Resumen

Let D be a link diagram with n crossings, sA and sB be its extreme states and |sAD| (respectively, |sBD|) be the number of simple closed curves that appear when smoothing D according to sA (respectively, sB). We give a general formula for the sum |sAD| + |sBD| for a k-almost alternating diagram D, for any k, characterizing this sum as the number of faces in an appropriate triangulation of an appropriate surface with boundary. When D is dealternator connected, the triangulation is especially simple, yielding |sAD| + |sBD| = n + 2 - 2k. This gives a simple geometric proof of the upper bound of the span of the Jones polynomial for dealternator connected diagrams, a result first obtained by Zhu [On Kauffman brackets, J. Knot Theory Ramifications6(1) (1997) 125–148.]. Another upper bound of the span of the Jones polynomial for dealternator connected and dealternator reduced diagrams, discovered historically first by Adams et al. [Almost alternating links, Topology Appl.46(2) (1992) 151–165.], is obtained as a corollary. As a new application, we prove that the Turaev genus is equal to the number k of dealternator crossings for any dealternator connected diagram

Más información

ID de Registro: 14153
Identificador DC: http://oa.upm.es/14153/
Identificador OAI: oai:oa.upm.es:14153
Identificador DOI: 10.1142/S0218216511009005
URL Oficial: http://www.worldscientific.com/doi/abs/10.1142/S0218216511009005?journalCode=jktr
Depositado por: Memoria Investigacion
Depositado el: 19 Dic 2012 10:58
Ultima Modificación: 21 Abr 2016 13:40
  • Open Access
  • Open Access
  • Sherpa-Romeo
    Compruebe si la revista anglosajona en la que ha publicado un artículo permite también su publicación en abierto.
  • Dulcinea
    Compruebe si la revista española en la que ha publicado un artículo permite también su publicación en abierto.
  • Recolecta
  • e-ciencia
  • Observatorio I+D+i UPM
  • OpenCourseWare UPM